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Properties

Label 16830.2
Level 16830
Weight 2
Dimension 1763336
Nonzero newspaces 144
Sturm bound 29859840

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Defining parameters

Level: \( N \) = \( 16830 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 144 \)
Sturm bound: \(29859840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(16830))\).

Total New Old
Modular forms 7505920 1763336 5742584
Cusp forms 7424001 1763336 5660665
Eisenstein series 81919 0 81919

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(16830))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16830.2.a \(\chi_{16830}(1, \cdot)\) 16830.2.a.a 1 1
16830.2.a.b 1
16830.2.a.c 1
16830.2.a.d 1
16830.2.a.e 1
16830.2.a.f 1
16830.2.a.g 1
16830.2.a.h 1
16830.2.a.i 1
16830.2.a.j 1
16830.2.a.k 1
16830.2.a.l 1
16830.2.a.m 1
16830.2.a.n 1
16830.2.a.o 1
16830.2.a.p 1
16830.2.a.q 1
16830.2.a.r 1
16830.2.a.s 1
16830.2.a.t 1
16830.2.a.u 1
16830.2.a.v 1
16830.2.a.w 1
16830.2.a.x 1
16830.2.a.y 1
16830.2.a.z 1
16830.2.a.ba 1
16830.2.a.bb 1
16830.2.a.bc 1
16830.2.a.bd 1
16830.2.a.be 1
16830.2.a.bf 1
16830.2.a.bg 1
16830.2.a.bh 1
16830.2.a.bi 1
16830.2.a.bj 1
16830.2.a.bk 1
16830.2.a.bl 1
16830.2.a.bm 1
16830.2.a.bn 1
16830.2.a.bo 1
16830.2.a.bp 1
16830.2.a.bq 1
16830.2.a.br 1
16830.2.a.bs 1
16830.2.a.bt 1
16830.2.a.bu 1
16830.2.a.bv 1
16830.2.a.bw 1
16830.2.a.bx 1
16830.2.a.by 1
16830.2.a.bz 1
16830.2.a.ca 1
16830.2.a.cb 1
16830.2.a.cc 1
16830.2.a.cd 1
16830.2.a.ce 1
16830.2.a.cf 1
16830.2.a.cg 1
16830.2.a.ch 1
16830.2.a.ci 1
16830.2.a.cj 1
16830.2.a.ck 1
16830.2.a.cl 1
16830.2.a.cm 1
16830.2.a.cn 1
16830.2.a.co 1
16830.2.a.cp 1
16830.2.a.cq 1
16830.2.a.cr 1
16830.2.a.cs 1
16830.2.a.ct 1
16830.2.a.cu 1
16830.2.a.cv 1
16830.2.a.cw 1
16830.2.a.cx 1
16830.2.a.cy 1
16830.2.a.cz 2
16830.2.a.da 2
16830.2.a.db 2
16830.2.a.dc 2
16830.2.a.dd 2
16830.2.a.de 2
16830.2.a.df 2
16830.2.a.dg 2
16830.2.a.dh 2
16830.2.a.di 2
16830.2.a.dj 2
16830.2.a.dk 2
16830.2.a.dl 2
16830.2.a.dm 2
16830.2.a.dn 2
16830.2.a.do 2
16830.2.a.dp 2
16830.2.a.dq 2
16830.2.a.dr 2
16830.2.a.ds 2
16830.2.a.dt 3
16830.2.a.du 3
16830.2.a.dv 3
16830.2.a.dw 3
16830.2.a.dx 3
16830.2.a.dy 3
16830.2.a.dz 3
16830.2.a.ea 3
16830.2.a.eb 3
16830.2.a.ec 3
16830.2.a.ed 3
16830.2.a.ee 3
16830.2.a.ef 3
16830.2.a.eg 3
16830.2.a.eh 3
16830.2.a.ei 3
16830.2.a.ej 3
16830.2.a.ek 3
16830.2.a.el 3
16830.2.a.em 3
16830.2.a.en 3
16830.2.a.eo 4
16830.2.a.ep 4
16830.2.a.eq 4
16830.2.a.er 4
16830.2.a.es 4
16830.2.a.et 4
16830.2.a.eu 4
16830.2.a.ev 4
16830.2.a.ew 4
16830.2.a.ex 4
16830.2.a.ey 4
16830.2.a.ez 5
16830.2.a.fa 5
16830.2.a.fb 5
16830.2.a.fc 5
16830.2.a.fd 6
16830.2.a.fe 6
16830.2.a.ff 8
16830.2.a.fg 8
16830.2.b \(\chi_{16830}(15641, \cdot)\) n/a 256 1
16830.2.d \(\chi_{16830}(10099, \cdot)\) n/a 400 1
16830.2.f \(\chi_{16830}(16829, \cdot)\) n/a 432 1
16830.2.h \(\chi_{16830}(7921, \cdot)\) n/a 300 1
16830.2.k \(\chi_{16830}(6731, \cdot)\) n/a 288 1
16830.2.m \(\chi_{16830}(1189, \cdot)\) n/a 452 1
16830.2.o \(\chi_{16830}(8909, \cdot)\) n/a 384 1
16830.2.q \(\chi_{16830}(5611, \cdot)\) n/a 1280 2
16830.2.r \(\chi_{16830}(3277, \cdot)\) n/a 1080 2
16830.2.t \(\chi_{16830}(10187, \cdot)\) n/a 720 2
16830.2.v \(\chi_{16830}(13069, \cdot)\) n/a 904 2
16830.2.x \(\chi_{16830}(1781, \cdot)\) n/a 576 2
16830.2.z \(\chi_{16830}(13157, \cdot)\) n/a 720 2
16830.2.bc \(\chi_{16830}(5237, \cdot)\) n/a 640 2
16830.2.bd \(\chi_{16830}(8227, \cdot)\) n/a 1080 2
16830.2.bg \(\chi_{16830}(307, \cdot)\) n/a 960 2
16830.2.bi \(\chi_{16830}(2971, \cdot)\) n/a 600 2
16830.2.bk \(\chi_{16830}(11879, \cdot)\) n/a 864 2
16830.2.bm \(\chi_{16830}(5257, \cdot)\) n/a 1080 2
16830.2.bo \(\chi_{16830}(8207, \cdot)\) n/a 720 2
16830.2.bp \(\chi_{16830}(3061, \cdot)\) n/a 1280 4
16830.2.bq \(\chi_{16830}(3299, \cdot)\) n/a 2304 2
16830.2.bt \(\chi_{16830}(1121, \cdot)\) n/a 1728 2
16830.2.bv \(\chi_{16830}(6799, \cdot)\) n/a 2160 2
16830.2.by \(\chi_{16830}(5609, \cdot)\) n/a 2592 2
16830.2.ca \(\chi_{16830}(2311, \cdot)\) n/a 1440 2
16830.2.cc \(\chi_{16830}(4421, \cdot)\) n/a 1536 2
16830.2.ce \(\chi_{16830}(4489, \cdot)\) n/a 1920 2
16830.2.cf \(\chi_{16830}(3959, \cdot)\) n/a 1728 4
16830.2.cg \(\chi_{16830}(1981, \cdot)\) n/a 1200 4
16830.2.cj \(\chi_{16830}(287, \cdot)\) n/a 1440 4
16830.2.ck \(\chi_{16830}(2287, \cdot)\) n/a 2160 4
16830.2.cp \(\chi_{16830}(5653, \cdot)\) n/a 2160 4
16830.2.cq \(\chi_{16830}(3653, \cdot)\) n/a 1440 4
16830.2.ct \(\chi_{16830}(5149, \cdot)\) n/a 1792 4
16830.2.cu \(\chi_{16830}(791, \cdot)\) n/a 1152 4
16830.2.cx \(\chi_{16830}(2789, \cdot)\) n/a 1536 4
16830.2.cz \(\chi_{16830}(4249, \cdot)\) n/a 2160 4
16830.2.db \(\chi_{16830}(611, \cdot)\) n/a 1152 4
16830.2.dc \(\chi_{16830}(3331, \cdot)\) n/a 1440 4
16830.2.de \(\chi_{16830}(4589, \cdot)\) n/a 1728 4
16830.2.dg \(\chi_{16830}(5509, \cdot)\) n/a 1920 4
16830.2.di \(\chi_{16830}(3401, \cdot)\) n/a 1024 4
16830.2.dk \(\chi_{16830}(1033, \cdot)\) n/a 5184 4
16830.2.dm \(\chi_{16830}(2333, \cdot)\) n/a 4320 4
16830.2.do \(\chi_{16830}(8581, \cdot)\) n/a 2880 4
16830.2.dq \(\chi_{16830}(659, \cdot)\) n/a 5184 4
16830.2.ds \(\chi_{16830}(2993, \cdot)\) n/a 3840 4
16830.2.dv \(\chi_{16830}(1937, \cdot)\) n/a 4320 4
16830.2.dw \(\chi_{16830}(5917, \cdot)\) n/a 4608 4
16830.2.dz \(\chi_{16830}(373, \cdot)\) n/a 5184 4
16830.2.eb \(\chi_{16830}(1849, \cdot)\) n/a 4320 4
16830.2.ed \(\chi_{16830}(7391, \cdot)\) n/a 3456 4
16830.2.ef \(\chi_{16830}(3013, \cdot)\) n/a 5184 4
16830.2.eh \(\chi_{16830}(353, \cdot)\) n/a 4320 4
16830.2.ei \(\chi_{16830}(511, \cdot)\) n/a 6144 8
16830.2.el \(\chi_{16830}(397, \cdot)\) n/a 3600 8
16830.2.em \(\chi_{16830}(1187, \cdot)\) n/a 3456 8
16830.2.ep \(\chi_{16830}(881, \cdot)\) n/a 1920 8
16830.2.eq \(\chi_{16830}(3871, \cdot)\) n/a 2880 8
16830.2.et \(\chi_{16830}(109, \cdot)\) n/a 4320 8
16830.2.eu \(\chi_{16830}(2069, \cdot)\) n/a 2880 8
16830.2.ev \(\chi_{16830}(197, \cdot)\) n/a 3456 8
16830.2.ew \(\chi_{16830}(793, \cdot)\) n/a 3600 8
16830.2.fa \(\chi_{16830}(1313, \cdot)\) n/a 3456 8
16830.2.fc \(\chi_{16830}(523, \cdot)\) n/a 4320 8
16830.2.fd \(\chi_{16830}(1619, \cdot)\) n/a 3456 8
16830.2.ff \(\chi_{16830}(361, \cdot)\) n/a 2880 8
16830.2.fh \(\chi_{16830}(613, \cdot)\) n/a 3840 8
16830.2.fk \(\chi_{16830}(2107, \cdot)\) n/a 4320 8
16830.2.fl \(\chi_{16830}(647, \cdot)\) n/a 3072 8
16830.2.fo \(\chi_{16830}(917, \cdot)\) n/a 3456 8
16830.2.fq \(\chi_{16830}(701, \cdot)\) n/a 2304 8
16830.2.fs \(\chi_{16830}(829, \cdot)\) n/a 4320 8
16830.2.ft \(\chi_{16830}(863, \cdot)\) n/a 3456 8
16830.2.fv \(\chi_{16830}(217, \cdot)\) n/a 4320 8
16830.2.fx \(\chi_{16830}(461, \cdot)\) n/a 6912 8
16830.2.fy \(\chi_{16830}(529, \cdot)\) n/a 8640 8
16830.2.gd \(\chi_{16830}(1607, \cdot)\) n/a 8640 8
16830.2.ge \(\chi_{16830}(43, \cdot)\) n/a 10368 8
16830.2.gf \(\chi_{16830}(637, \cdot)\) n/a 10368 8
16830.2.gg \(\chi_{16830}(3323, \cdot)\) n/a 8640 8
16830.2.gl \(\chi_{16830}(331, \cdot)\) n/a 5760 8
16830.2.gm \(\chi_{16830}(3629, \cdot)\) n/a 10368 8
16830.2.go \(\chi_{16830}(1939, \cdot)\) n/a 9216 8
16830.2.gq \(\chi_{16830}(1361, \cdot)\) n/a 6144 8
16830.2.gs \(\chi_{16830}(1291, \cdot)\) n/a 6912 8
16830.2.gu \(\chi_{16830}(1019, \cdot)\) n/a 10368 8
16830.2.gv \(\chi_{16830}(169, \cdot)\) n/a 10368 8
16830.2.gx \(\chi_{16830}(101, \cdot)\) n/a 6912 8
16830.2.ha \(\chi_{16830}(239, \cdot)\) n/a 9216 8
16830.2.hc \(\chi_{16830}(559, \cdot)\) n/a 8640 16
16830.2.hd \(\chi_{16830}(161, \cdot)\) n/a 4608 16
16830.2.hi \(\chi_{16830}(127, \cdot)\) n/a 8640 16
16830.2.hj \(\chi_{16830}(773, \cdot)\) n/a 6912 16
16830.2.hk \(\chi_{16830}(53, \cdot)\) n/a 6912 16
16830.2.hl \(\chi_{16830}(937, \cdot)\) n/a 8640 16
16830.2.hq \(\chi_{16830}(359, \cdot)\) n/a 6912 16
16830.2.hr \(\chi_{16830}(631, \cdot)\) n/a 5760 16
16830.2.hu \(\chi_{16830}(1057, \cdot)\) n/a 17280 16
16830.2.hv \(\chi_{16830}(857, \cdot)\) n/a 20736 16
16830.2.hw \(\chi_{16830}(419, \cdot)\) n/a 17280 16
16830.2.hx \(\chi_{16830}(439, \cdot)\) n/a 20736 16
16830.2.ia \(\chi_{16830}(241, \cdot)\) n/a 13824 16
16830.2.ib \(\chi_{16830}(551, \cdot)\) n/a 11520 16
16830.2.ie \(\chi_{16830}(3497, \cdot)\) n/a 20736 16
16830.2.if \(\chi_{16830}(133, \cdot)\) n/a 17280 16
16830.2.ij \(\chi_{16830}(1373, \cdot)\) n/a 20736 16
16830.2.il \(\chi_{16830}(1993, \cdot)\) n/a 20736 16
16830.2.im \(\chi_{16830}(761, \cdot)\) n/a 13824 16
16830.2.io \(\chi_{16830}(2869, \cdot)\) n/a 20736 16
16830.2.iq \(\chi_{16830}(1393, \cdot)\) n/a 20736 16
16830.2.it \(\chi_{16830}(1327, \cdot)\) n/a 18432 16
16830.2.iu \(\chi_{16830}(203, \cdot)\) n/a 20736 16
16830.2.ix \(\chi_{16830}(137, \cdot)\) n/a 18432 16
16830.2.iz \(\chi_{16830}(149, \cdot)\) n/a 20736 16
16830.2.jb \(\chi_{16830}(421, \cdot)\) n/a 13824 16
16830.2.jc \(\chi_{16830}(47, \cdot)\) n/a 20736 16
16830.2.je \(\chi_{16830}(13, \cdot)\) n/a 20736 16
16830.2.ji \(\chi_{16830}(37, \cdot)\) n/a 17280 32
16830.2.jj \(\chi_{16830}(233, \cdot)\) n/a 13824 32
16830.2.jk \(\chi_{16830}(541, \cdot)\) n/a 11520 32
16830.2.jl \(\chi_{16830}(71, \cdot)\) n/a 9216 32
16830.2.jo \(\chi_{16830}(269, \cdot)\) n/a 13824 32
16830.2.jp \(\chi_{16830}(469, \cdot)\) n/a 17280 32
16830.2.js \(\chi_{16830}(107, \cdot)\) n/a 13824 32
16830.2.jt \(\chi_{16830}(487, \cdot)\) n/a 17280 32
16830.2.jw \(\chi_{16830}(841, \cdot)\) n/a 27648 32
16830.2.jx \(\chi_{16830}(569, \cdot)\) n/a 41472 32
16830.2.ka \(\chi_{16830}(457, \cdot)\) n/a 41472 32
16830.2.kb \(\chi_{16830}(587, \cdot)\) n/a 41472 32
16830.2.kg \(\chi_{16830}(257, \cdot)\) n/a 41472 32
16830.2.kh \(\chi_{16830}(733, \cdot)\) n/a 41472 32
16830.2.kk \(\chi_{16830}(281, \cdot)\) n/a 27648 32
16830.2.kl \(\chi_{16830}(49, \cdot)\) n/a 41472 32
16830.2.ko \(\chi_{16830}(367, \cdot)\) n/a 82944 64
16830.2.kp \(\chi_{16830}(167, \cdot)\) n/a 82944 64
16830.2.ks \(\chi_{16830}(79, \cdot)\) n/a 82944 64
16830.2.kt \(\chi_{16830}(779, \cdot)\) n/a 82944 64
16830.2.kw \(\chi_{16830}(311, \cdot)\) n/a 55296 64
16830.2.kx \(\chi_{16830}(61, \cdot)\) n/a 55296 64
16830.2.ky \(\chi_{16830}(173, \cdot)\) n/a 82944 64
16830.2.kz \(\chi_{16830}(97, \cdot)\) n/a 82944 64

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(16830))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(16830)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(765))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1122))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1530))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1683))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1870))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2805))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8415))\)\(^{\oplus 2}\)